Differential and Integral Calculus (Classic Reprint)

This book presents a first course in the calculus substantially as the author has taught it at the University of Michigan for a number of years. The following points may be mentioned as more or less prominent features of the book.

In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the student's clear understanding of this principle, without distracting his attention by the discussion of a multitude of details. The accompanying exercises are intended to present the problem in hand in a great variety of forms and guises, and to train the student in adapting the general methods of the text to fit these various forms. The constant aim is to prevent the work from degenerating into mere mechanical routine, as it so often tends to do. Wherever possible, except in the purely formal parts of the course, the summarizing of the theory into rules or formulas which can be applied blindly has been avoided. For instance, in the chapter on geometric applications of the definite integral, stress is laid on the fact that the basic formulas are those of elementary geometry, and special formulas involving a coordinate system are omitted.

Where the passage from theory to practice would be too difficult for the average student, worked examples are inserted.

Tags: curve equation ans function sin cos plane functions line integral axis calculus limit log equations differential hence surface terms tangent
Category: Mathematics - Calculus

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